%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA027-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 19:28:52 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of clauses : 30 ( 12 unt; 0 nHn; 30 RR)
% Number of literals : 54 ( 0 equ; 31 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(u)
| equal(c_plus(c_0,v,u),v) ),
file('ANA027-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(u)
| ~ c_lessequals(v,c_minus(w,x,u),u)
| c_lessequals(c_plus(v,x,u),w,u) ),
file('ANA027-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(u)
| ~ c_lessequals(c_plus(v,w,u),x,u)
| c_lessequals(v,c_minus(x,w,u),u) ),
file('ANA027-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(w,x,u)
| c_lessequals(v,x,u) ),
file('ANA027-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_LOrder_Ojoin__semilorder(u)
| class_Orderings_Oorder(u) ),
file('ANA027-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| class_OrderedGroup_Opordered__ab__group__add(u) ),
file('ANA027-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| class_LOrder_Ojoin__semilorder(u) ),
file('ANA027-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Ocomm__monoid__add(u) ),
file('ANA027-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA027-2.p',unknown),
[] ).
cnf(10,axiom,
c_lessequals(c_0,c_minus(v(v_x),v_k(v_x),t_b),t_b),
file('ANA027-2.p',unknown),
[] ).
cnf(11,axiom,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
file('ANA027-2.p',unknown),
[] ).
cnf(12,axiom,
~ c_lessequals(c_0,c_minus(v(v_x),v_g(v_x),t_b),t_b),
file('ANA027-2.p',unknown),
[] ).
cnf(13,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA027-2.p',unknown),
[] ).
cnf(14,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(res,[status(thm),theory(equality)],[13,8]),
[iquote('0:Res:13.0,8.0')] ).
cnf(15,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(res,[status(thm),theory(equality)],[13,9]),
[iquote('0:Res:13.0,9.0')] ).
cnf(17,plain,
( ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(v_k(v_x),u,t_b)
| c_lessequals(v_g(v_x),u,t_b) ),
inference(res,[status(thm),theory(equality)],[11,4]),
[iquote('0:Res:11.0,4.2')] ).
cnf(19,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v(v_x),t_b) ),
inference(res,[status(thm),theory(equality)],[10,2]),
[iquote('0:Res:10.0,2.1')] ).
cnf(21,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v(v_x),t_b) ),
inference(res,[status(thm),theory(equality)],[3,12]),
[iquote('0:Res:3.2,12.0')] ).
cnf(26,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v(v_x),t_b) ),
inference(sor,[status(thm)],[19,6]),
[iquote('0:SoR:19.0,6.1')] ).
cnf(27,plain,
c_lessequals(c_plus(c_0,v_k(v_x),t_b),v(v_x),t_b),
inference(ssi,[status(thm)],[26,13,14,15]),
[iquote('0:SSi:26.0,13.0,14.0,15.0')] ).
cnf(28,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| c_lessequals(v_k(v_x),v(v_x),t_b) ),
inference(spr,[status(thm),theory(equality)],[1,27]),
[iquote('0:SpR:1.1,27.0')] ).
cnf(29,plain,
c_lessequals(v_k(v_x),v(v_x),t_b),
inference(ssi,[status(thm)],[28,13,14,15]),
[iquote('0:SSi:28.0,13.0,14.0,15.0')] ).
cnf(38,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v(v_x),t_b) ),
inference(sor,[status(thm)],[21,6]),
[iquote('0:SoR:21.0,6.1')] ).
cnf(39,plain,
~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v(v_x),t_b),
inference(ssi,[status(thm)],[38,13,14,15]),
[iquote('0:SSi:38.0,13.0,14.0,15.0')] ).
cnf(40,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ~ c_lessequals(v_g(v_x),v(v_x),t_b) ),
inference(spl,[status(thm),theory(equality)],[1,39]),
[iquote('0:SpL:1.1,39.0')] ).
cnf(41,plain,
~ c_lessequals(v_g(v_x),v(v_x),t_b),
inference(ssi,[status(thm)],[40,13,14,15]),
[iquote('0:SSi:40.0,13.0,14.0,15.0')] ).
cnf(45,plain,
( ~ class_LOrder_Ojoin__semilorder(t_b)
| ~ c_lessequals(v_k(v_x),u,t_b)
| c_lessequals(v_g(v_x),u,t_b) ),
inference(sor,[status(thm)],[17,5]),
[iquote('0:SoR:17.0,5.1')] ).
cnf(46,plain,
( ~ c_lessequals(v_k(v_x),u,t_b)
| c_lessequals(v_g(v_x),u,t_b) ),
inference(ssi,[status(thm)],[45,7,13,14,15]),
[iquote('0:SSi:45.0,7.0,13.0,14.0,15.1')] ).
cnf(47,plain,
~ c_lessequals(v_k(v_x),v(v_x),t_b),
inference(res,[status(thm),theory(equality)],[46,41]),
[iquote('0:Res:46.1,41.0')] ).
cnf(49,plain,
$false,
inference(mrr,[status(thm)],[47,29]),
[iquote('0:MRR:47.0,29.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ANA027-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 06:16:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.40
% 0.19/0.40 SPASS V 3.9
% 0.19/0.40 SPASS beiseite: Proof found.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.40 SPASS derived 27 clauses, backtracked 0 clauses, performed 0 splits and kept 35 clauses.
% 0.19/0.40 SPASS allocated 75646 KBytes.
% 0.19/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.40 0:00:00.03 for the input.
% 0.19/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40 0:00:00.00 for inferences.
% 0.19/0.40 0:00:00.00 for the backtracking.
% 0.19/0.40 0:00:00.00 for the reduction.
% 0.19/0.40
% 0.19/0.40
% 0.19/0.40 Here is a proof with depth 4, length 30 :
% 0.19/0.40 % SZS output start Refutation
% See solution above
% 0.19/0.40 Formulae used in the proof : cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0 cls_OrderedGroup_Ocompare__rls__9_0 cls_OrderedGroup_Ocompare__rls__9_1 cls_Orderings_Oorder__class_Oorder__trans_0 clsrel_LOrder_Ojoin__semilorder_1 clsrel_OrderedGroup_Olordered__ab__group__abs_1 clsrel_OrderedGroup_Olordered__ab__group__abs_15 clsrel_Ring__and__Field_Oordered__idom_23 clsrel_Ring__and__Field_Oordered__idom_50 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 tfree_tcs
% 0.19/0.40
%------------------------------------------------------------------------------